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Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem. (English) Zbl 0507.65027

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
65F50 Computational methods for sparse matrices
Full Text: DOI
[1] J.A. Bondy and U.S.R. Murty,Graph theory with applications (MacMillan, London, 1976). · Zbl 1226.05083
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[5] G.R. Grimmet and C.J.H. McDiarmid, ”On colouring random graphs”,Proceedings of the Cambridge Philosophical Society 77 (1975) 313–324. · Zbl 0297.05112
[6] D.S. Johnson, ”Worst case behavior of graph coloring algorithms”. in:Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory, and Computing (Utilitas Mathematica, Winnipeg. Man., 1974) pp. 513–527. · Zbl 0308.05109
[7] R.M. Karp, ”Reducibility among combinatorial problems” in: R.E. Miller and J.W. Thatcher, eds.,Complexity of computer computations (Plenum, New York, 1972) pp. 85–103.
[8] M.J.D. Powell and P.L. Toint, ”On the estimation of sparse Hessian matrices”,SIAM Journal on Numerical Analysis 16 (1979), 1060–1074. · Zbl 0426.65025
[9] M.N. Thapa, ”Optimization of unconstrained functions with sparse Hessian matrices”, Ph.D. Thesis, Stanford University (Stanford, CA, 1980).
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